Let  be a prime ring,  be a non-zero ideal of  and   be automorphism on. A mapping  is called a multiplicative (generalized)  reverse derivation if  where  is any map (not necessarily additive). In this paper, we proved the commutativity of a prime ring R admitting a multiplicative (generalized)  reverse derivation  satisfying any one of the properties:

 for all x, y  

     World statistics declare that aging has direct correlations with more and more health problems with comorbid conditions. As healthcare communities evolve with a massive amount of data at a faster pace, it is essential to predict, assist, and prevent diseases at the right time, especially for elders. Similarly, many researchers have discussed that elders suffer extensively due to chronic health conditions.  This work was performed to review literature studies on prediction systems for various chronic illnesses of elderly people. Most of the reviewed papers proposed machine learning prediction models combined with, or without, other related intelligence techniques for chronic disease detection of elderly patie

In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi